The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  2  2  1  2  1  1  4  1  2  4  1  4  2  2  1  2  4  2  1  1  1  1  1  1  2  1
 0 12  0  0  0  0  0  0  0  4 12 12  4  8  8 12  8  0 12 12  4  4  0 12  8  4 12  4 12  0 12  8  8  0 12  8  0  8  8  0 12  8  4 12  0  4  0  0  8 12 12 12  4 12  4  8 12 12  4  0  8  4  4  4 12  4  8 12  4 12
 0  0 12  0  0  0  4 12 12  4  4  0  8  0 12 12 12  8  8 12  4 12 12  0  0  4 12  8  0  4  8  0  8  0 12  8  0 12  0  8  8  4  4  0  4  8 12  4  8  0  4  8 12  8  8 12  4 12 12  8  8 12  4  8  4  4  8  8  0  4
 0  0  0 12  0  4  4  4  0  8  0  8 12  0  0 12 12  8  4 12 12  0  4  4 12  0  4  8  8  8  4  4  4  0 12  0  4 12  4  0  0  4  4 12 12  4  0  4  4  8  4  0  8 12  0  8  8  4 12 12  4  0  0  8  0 12 12 12  8  0
 0  0  0  0 12  4  8  4  4  0  4  4  0  0  8  4 12 12  4  4  8  4  0  8  4  0  8 12  8 12 12  0  0  0  8 12 12  0  4  0  4  4  4  8  0  0  8  8  8 12  0  4  0 12  8  4  4  4  4  0  4 12  8  4 12  8  0  0 12 12
 0  0  0  0  0  8  8  0  8  8  8  0  8  8  8  8  8  8  0  0  8  0  0  0  0  0  0  8  8  0  8  8  0  8  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  8  8  0  0  8  8  0  0  8  8  0  0  0  0  8  0  8  0  0  0

generates a code of length 70 over Z16 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+56x^61+101x^62+134x^63+172x^64+198x^65+225x^66+446x^67+742x^68+1272x^69+1665x^70+1158x^71+730x^72+500x^73+226x^74+142x^75+114x^76+84x^77+48x^78+60x^79+29x^80+30x^81+33x^82+12x^83+4x^84+4x^85+5x^86+1x^110

The gray image is a code over GF(2) with n=560, k=13 and d=244.
This code was found by Heurico 1.16 in 2.14 seconds.